Abstract

Building upon the work of Wei and Ge (Designs, Codes,and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type gum1 are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m > 0 and m ≠ g are suﬃcient in the following cases: g ≡ 0 (mod 6), g =2 with one exception, 2651, g =10, and g =11.